How to make rocket engine plume?
If you have a nice computer, look into smoke simulation

Although, any flames that you make in space are going to look a little bit fake, because most people have never seen flames in space 

Ignoring the awful camera quality, https://www.youtube.com/watch?v=FEom0G30Gic is the type of thing that it seems like you are trying to emulate. If you want realism, I would do a quick fire thing like you have, and then overexpose the video while the fire takes up most of the screen.
Your also missing the camera shake from the rocket, your footage is unnaturally smooth.